Question

(i) 5^{log 4} = 4^{log 5}

(ii) If `x = log  1/2, y = log  2/3`, z = log 3, then x + y + z = 0

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

(i) Take log of both sides:

`log(5^(log 4)) `

= (log 4)(log 5) 

= `log(4^(log 5))` 

So the two numbers have the same log and are equal.

(ii) `x = log (1/2)`

= –log 2

`y = log (2/3)`

= log 2 – log 3 

z = log 3

Summing:

(–log 2) + (log 2 – log 3) + log 3 = 0